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New Mirzakhani-type identities for the simple hyperbolic length spectrum

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Gaetan Borot
Die, 2018-07-10 14:00 - 15:00
MPIM Lecture Hall

McShane obtained in 1991 an identity expressing the function 1 on the Teichmueller space of the once-punctured torus as a sum over simple closed curves. It was generalized to bordered surfaces of all topologies by Mirzakhani in 2005, from which she deduced a topological recursion for the Weil-Petersson volumes. Using Mirzakhani identities as a partition of unity, I will present new identities which represent linear statistics of the simple length spectrum as a sum over homotopy class of pairs of pants in a hyperbolic surface, from which one can deduce a topological recursion for their average over the moduli space. This is an example of application of a geometric recursion developed with Andersen and Orantin.


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